Modeller

MSB 105 - Assignment 4

suppressPackageStartupMessages({
library(tidyverse)
library(lubridate)
library(modelr)
library(broom)
library(lmtest)
library(sandwich)
library(viridis)
})

Henter csv. filen:

pm2 <- read_csv("data/pm2.csv", show_col_types = FALSE)

New names:
* `` -> ...1

Muterer:

pm2 <- pm2 %>% 
  mutate(
    fnr = str_sub(knr, 1,2),
    aar_f = str_sub(aar)
  )

head(pm2)

parse_factor funksjonen:

pm2 %>% 
  mutate(
    fnr = parse_factor(fnr, levels = fnr),
    aar_f = parse_factor(aar_f, levels = aar_f)
  )

muterer:

pm2 <- pm2 %>% 
  mutate(
    Trade_pc_100K = Trade_p/100000
  ) 

head(pm2, n = 4)

Modell

mod1 <- 'pm2 ~ aar_f + Total_ya_p + inc_k1 + inc_k5 + uni_k_mf + uni_l_mf + Trade_pc_100K'

lm1 <- lm(mod1, data = pm2, subset = complete.cases(pm2))

summary(lm1)

Call:
lm(formula = mod1, data = pm2, subset = complete.cases(pm2))

Residuals:
    Min      1Q  Median      3Q     Max 
-8516.6 -1472.1   -29.9  1467.3 15736.3 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -20400.74    2663.02  -7.661 2.79e-14 ***
aar_f2009        104.15     244.77   0.426 0.670512    
aar_f2010        908.13     245.16   3.704 0.000217 ***
aar_f2011       1663.93     245.86   6.768 1.68e-11 ***
aar_f2012       2240.48     247.10   9.067  < 2e-16 ***
aar_f2013       2869.30     248.31  11.555  < 2e-16 ***
aar_f2014       2863.22     250.54  11.428  < 2e-16 ***
aar_f2015       3525.22     253.08  13.929  < 2e-16 ***
aar_f2016       4274.99     255.81  16.711  < 2e-16 ***
aar_f2017       5146.33     258.50  19.909  < 2e-16 ***
Total_ya_p       582.44      38.94  14.957  < 2e-16 ***
inc_k1          -376.99      30.29 -12.445  < 2e-16 ***
inc_k5           194.35      22.87   8.498  < 2e-16 ***
uni_k_mf         -82.02      29.42  -2.788 0.005357 ** 
uni_l_mf        1206.86      42.22  28.585  < 2e-16 ***
Trade_pc_100K    871.99     218.42   3.992 6.77e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2531 on 2124 degrees of freedom
Multiple R-squared:  0.8346,    Adjusted R-squared:  0.8334 
F-statistic: 714.3 on 15 and 2124 DF,  p-value: < 2.2e-16

2. Legger til residualer:

pm2 %>% 
  add_residuals(lm1)

head(pm2, n = 4)

Man leser ut gjennomsnittlig kvadratmeterpris for en enebolig (\(pm2\)) for de forskjellige årene. Vi ser at \(pm2\) stiger jevnt og trutt.

Vi vil si at fortegnene er som forventet. Dersom vi har tolket modellen riktig, så vil \(pm2\) være mindre for dem nederste kvintilen (inc_k1) enn for den øverste (inc_k5). Det samme gjelder for de med kort og lang utdanning.

Dette er nok fordi den rikere delen av befolkninge, og de med høyere utdanning, sannsynligvis har mer attraktive eneboliger som gjør at \(pm2\) er høyere.

Heteroskedastisitet

i.

bptest(lm1)

    studentized Breusch-Pagan test

data:  lm1
BP = 352.89, df = 15, p-value < 2.2e-16

ii.

Veldig høy p-verdi. Da kan \(H_0\) forkastes og vi kan med sterke bevis si at det foreligger Heteroskedastisitet.

iii.

coeftest(lm1)

t test of coefficients:

                Estimate Std. Error  t value  Pr(>|t|)    
(Intercept)   -20400.742   2663.022  -7.6607 2.790e-14 ***
aar_f2009        104.150    244.767   0.4255 0.6705118    
aar_f2010        908.129    245.156   3.7043 0.0002174 ***
aar_f2011       1663.926    245.857   6.7679 1.685e-11 ***
aar_f2012       2240.475    247.095   9.0672 < 2.2e-16 ***
aar_f2013       2869.297    248.315  11.5551 < 2.2e-16 ***
aar_f2014       2863.224    250.537  11.4283 < 2.2e-16 ***
aar_f2015       3525.223    253.083  13.9291 < 2.2e-16 ***
aar_f2016       4274.990    255.812  16.7114 < 2.2e-16 ***
aar_f2017       5146.326    258.498  19.9086 < 2.2e-16 ***
Total_ya_p       582.436     38.941  14.9568 < 2.2e-16 ***
inc_k1          -376.989     30.291 -12.4455 < 2.2e-16 ***
inc_k5           194.354     22.871   8.4979 < 2.2e-16 ***
uni_k_mf         -82.023     29.424  -2.7876 0.0053574 ** 
uni_l_mf        1206.857     42.219  28.5853 < 2.2e-16 ***
Trade_pc_100K    871.993    218.422   3.9922 6.768e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

vcovHC(lm1)

              (Intercept)    aar_f2009   aar_f2010   aar_f2011   aar_f2012
(Intercept)    9297989.37 -26519.17426 -34751.3931 -64358.9799 -88195.7750
aar_f2009       -26519.17  42579.51052  22306.6988  22379.0191  22461.1963
aar_f2010       -34751.39  22306.69876  41857.2132  22643.0594  22816.5776
aar_f2011       -64358.98  22379.01911  22643.0594  45210.7304  23406.9880
aar_f2012       -88195.78  22461.19628  22816.5776  23406.9880  47055.4187
aar_f2013       -93332.22  22562.49160  23016.0483  23690.1311  24270.5328
aar_f2014      -128032.51  22647.20878  23232.1454  24076.5421  24791.9383
aar_f2015      -177893.27  22637.74268  23267.9132  24237.7165  25055.0255
aar_f2016      -229170.12  22623.80635  23323.0788  24446.1520  25385.7301
aar_f2017      -231919.09  22624.44448  23352.3686  24515.4258  25408.7607
Total_ya_p     -134378.95     89.41919    277.8154    681.8928   1112.5721
inc_k1          -48847.48    -46.78668   -117.7882    188.8338    193.4766
inc_k5          -26724.41    110.78484    126.8286    397.1950    455.5137
uni_k_mf        -23624.40   -129.42390   -212.3787   -468.5265   -572.7298
uni_l_mf         79213.28    -45.36231   -237.3954   -324.3915   -491.9711
Trade_pc_100K   145568.84    497.16540   1261.8579    987.3383    936.1196
                 aar_f2013    aar_f2014    aar_f2015    aar_f2016    aar_f2017
(Intercept)   -93332.21682 -128032.5143 -177893.2733 -229170.1243 -231919.0869
aar_f2009      22562.49160   22647.2088   22637.7427   22623.8064   22624.4445
aar_f2010      23016.04825   23232.1454   23267.9132   23323.0788   23352.3686
aar_f2011      23690.13111   24076.5421   24237.7165   24446.1520   24515.4258
aar_f2012      24270.53282   24791.9383   25055.0255   25385.7301   25408.7607
aar_f2013      49220.90256   25428.8815   25755.4473   26135.5595   26169.5465
aar_f2014      25428.88146   53475.4422   27156.8674   27482.0673   27045.3309
aar_f2015      25755.44730   27156.8674   63394.1122   28309.5656   27655.2812
aar_f2016      26135.55952   27482.0673   28309.5656   75087.4602   28071.1160
aar_f2017      26169.54649   27045.3309   27655.2812   28071.1160   89424.5717
Total_ya_p      1311.74280    1662.7240    2349.7551    3130.9906    3266.6554
inc_k1           -23.25608     237.9932     438.1822     706.9105     723.9683
inc_k5           419.80206     750.9501     927.6337    1166.2786    1178.1709
uni_k_mf        -695.90501    -198.2867     136.4018    -110.1222    -816.2879
uni_l_mf        -632.27758   -2195.0185   -3034.7846   -2540.7427   -1110.7783
Trade_pc_100K   2510.69810    2684.4013    2764.2300     282.6406    1862.4720
                 Total_ya_p       inc_k1      inc_k5     uni_k_mf    uni_l_mf
(Intercept)   -134378.94615 -48847.47803 -26724.4053 -23624.40438 79213.27980
aar_f2009          89.41919    -46.78668    110.7848   -129.42390   -45.36231
aar_f2010         277.81538   -117.78822    126.8286   -212.37867  -237.39541
aar_f2011         681.89276    188.83384    397.1950   -468.52650  -324.39148
aar_f2012        1112.57212    193.47663    455.5137   -572.72977  -491.97106
aar_f2013        1311.74280    -23.25608    419.8021   -695.90501  -632.27758
aar_f2014        1662.72401    237.99318    750.9501   -198.28673 -2195.01848
aar_f2015        2349.75511    438.18220    927.6337    136.40176 -3034.78456
aar_f2016        3130.99055    706.91052   1166.2786   -110.12216 -2540.74265
aar_f2017        3266.65535    723.96826   1178.1709   -816.28793 -1110.77830
Total_ya_p       2167.75020    426.37025    133.2185     51.21924  -614.02732
inc_k1            426.37025    801.89764    496.4444    158.26504  -500.25996
inc_k5            133.21845    496.44438    547.3448    104.53767  -690.28424
uni_k_mf           51.21924    158.26504    104.5377   1515.96690 -2398.54359
uni_l_mf         -614.02732   -500.25996   -690.2842  -2398.54359  5463.68941
Trade_pc_100K   -1619.34164  -2293.03278   -115.1786  -2608.77275   651.94105
              Trade_pc_100K
(Intercept)     145568.8365
aar_f2009          497.1654
aar_f2010         1261.8579
aar_f2011          987.3383
aar_f2012          936.1196
aar_f2013         2510.6981
aar_f2014         2684.4013
aar_f2015         2764.2300
aar_f2016          282.6406
aar_f2017         1862.4720
Total_ya_p       -1619.3416
inc_k1           -2293.0328
inc_k5            -115.1786
uni_k_mf         -2608.7728
uni_l_mf           651.9410
Trade_pc_100K    60897.1826

iv.

pm2 <- pm2 %>% 
  add_residuals(lm1)

v.

pm2 <- pm2 %>%
  mutate(aar_d = make_date(aar))

vi.

pm2 <- pm2 %>%
  mutate(fylke = substr(knr, start = 1, stop = 2)) 

vii -x.

pm2 %>%
  filter(fylke %in% c("01", "02", "03", "11", "12")) %>% 
  unnest(c(fylke)) %>%
  group_by(fylke, aar_d) %>%
  summarize(mean_fylke = mean(resid)
            ) %>% 
  ggplot(aes(x = aar_d, y = mean_fylke, colour = fylke)) +
  geom_line(lwd=1) +
  theme(legend.position = "bottom")+
  geom_hline(yintercept = 0, colour = "black")

`summarise()` has grouped output by 'fylke'. You can override using the `.groups` argument.

Dummy fylke og år

i & ii.

mod2 <- 'pm2 ~ aar_f*fnr + Total_ya_p + inc_k1 + inc_k5 + uni_k_mf + uni_l_mf + Trade_pc_100K'

lm2 <- lm(mod2, data = pm2)

summary(lm2)

Call:
lm(formula = mod2, data = pm2)

Residuals:
   Min     1Q Median     3Q    Max 
 -8546  -1191     32   1198   8328 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)     -21200.688   2521.645  -8.407  < 2e-16 ***
aar_f2009           94.009    744.240   0.126 0.899496    
aar_f2010          417.129    744.379   0.560 0.575290    
aar_f2011         1280.914    744.731   1.720 0.085597 .  
aar_f2012         1455.525    745.679   1.952 0.051088 .  
aar_f2013         2479.533    746.367   3.322 0.000910 ***
aar_f2014         2795.831    747.254   3.741 0.000188 ***
aar_f2015         3987.973    748.109   5.331 1.09e-07 ***
aar_f2016         5264.965    749.169   7.028 2.89e-12 ***
aar_f2017         6618.572    749.430   8.831  < 2e-16 ***
fnr02            -1482.789    702.970  -2.109 0.035045 *  
fnr03             3248.234   2190.443   1.483 0.138260    
fnr04            -1049.219    774.264  -1.355 0.175537    
fnr05            -1937.388    758.293  -2.555 0.010696 *  
fnr06            -2172.731    772.094  -2.814 0.004941 ** 
fnr07             -737.995   1080.348  -0.683 0.494620    
fnr08            -3213.279    878.620  -3.657 0.000262 ***
fnr09            -1219.813    913.691  -1.335 0.182020    
fnr10             -281.375    852.265  -0.330 0.741323    
fnr11             -565.360    771.927  -0.732 0.464012    
fnr12             -903.071    742.464  -1.216 0.224012    
fnr14            -3339.829   1182.013  -2.826 0.004768 ** 
fnr15            -3619.198    715.832  -5.056 4.69e-07 ***
fnr16            -1093.217    759.677  -1.439 0.150296    
fnr17            -2005.965    917.216  -2.187 0.028860 *  
fnr18            -1567.503    774.530  -2.024 0.043126 *  
fnr19            -2856.881   1326.142  -2.154 0.031341 *  
fnr20            -2656.315   1180.088  -2.251 0.024500 *  
Total_ya_p         511.787     36.100  14.177  < 2e-16 ***
inc_k1            -243.050     27.007  -9.000  < 2e-16 ***
inc_k5             251.645     22.916  10.981  < 2e-16 ***
uni_k_mf           178.253     28.157   6.331 3.02e-10 ***
uni_l_mf           732.442     42.235  17.342  < 2e-16 ***
Trade_pc_100K     1067.760    190.885   5.594 2.54e-08 ***
aar_f2009:fnr02    -40.505    978.026  -0.041 0.966969    
aar_f2010:fnr02    792.694    978.020   0.811 0.417747    
aar_f2011:fnr02    992.480    978.070   1.015 0.310359    
aar_f2012:fnr02   1565.161    978.102   1.600 0.109716    
aar_f2013:fnr02   1953.373    978.298   1.997 0.045996 *  
aar_f2014:fnr02   2019.269    978.649   2.063 0.039214 *  
aar_f2015:fnr02   2401.120    979.036   2.453 0.014273 *  
aar_f2016:fnr02   3656.344    979.067   3.735 0.000193 ***
aar_f2017:fnr02   4707.776    979.374   4.807 1.65e-06 ***
aar_f2009:fnr03     84.133   3068.211   0.027 0.978127    
aar_f2010:fnr03   2004.378   3068.354   0.653 0.513677    
aar_f2011:fnr03   3891.025   3068.768   1.268 0.204970    
aar_f2012:fnr03   5674.403   3069.281   1.849 0.064642 .  
aar_f2013:fnr03   5108.375   3070.149   1.664 0.096297 .  
aar_f2014:fnr03   4938.603   3071.105   1.608 0.107979    
aar_f2015:fnr03   6985.367   3073.112   2.273 0.023131 *  
aar_f2016:fnr03  10264.572   3074.072   3.339 0.000856 ***
aar_f2017:fnr03  13986.613   3075.071   4.548 5.74e-06 ***
aar_f2009:fnr04   -330.219   1089.318  -0.303 0.761813    
aar_f2010:fnr04   -191.813   1089.355  -0.176 0.860250    
aar_f2011:fnr04   -775.700   1089.399  -0.712 0.476523    
aar_f2012:fnr04   -808.528   1089.510  -0.742 0.458115    
aar_f2013:fnr04  -1206.685   1089.615  -1.107 0.268240    
aar_f2014:fnr04  -1456.367   1089.708  -1.336 0.181550    
aar_f2015:fnr04  -1912.336   1089.754  -1.755 0.079446 .  
aar_f2016:fnr04  -2459.017   1089.893  -2.256 0.024169 *  
aar_f2017:fnr04  -3549.658   1089.920  -3.257 0.001146 ** 
aar_f2009:fnr05    416.862   1069.758   0.390 0.696816    
aar_f2010:fnr05    655.342   1069.794   0.613 0.540221    
aar_f2011:fnr05    183.865   1069.834   0.172 0.863563    
aar_f2012:fnr05    820.104   1070.017   0.766 0.443507    
aar_f2013:fnr05   -198.536   1070.094  -0.186 0.852832    
aar_f2014:fnr05   -254.055   1070.253  -0.237 0.812388    
aar_f2015:fnr05  -1326.089   1070.254  -1.239 0.215480    
aar_f2016:fnr05  -2117.228   1070.338  -1.978 0.048059 *  
aar_f2017:fnr05  -2397.820   1070.176  -2.241 0.025165 *  
aar_f2009:fnr06   -163.759   1089.292  -0.150 0.880516    
aar_f2010:fnr06    189.332   1089.409   0.174 0.862046    
aar_f2011:fnr06     33.963   1089.394   0.031 0.975132    
aar_f2012:fnr06    800.976   1089.455   0.735 0.462302    
aar_f2013:fnr06    410.281   1089.375   0.377 0.706497    
aar_f2014:fnr06    571.152   1089.474   0.524 0.600167    
aar_f2015:fnr06     22.631   1089.626   0.021 0.983431    
aar_f2016:fnr06   -598.671   1089.701  -0.549 0.582801    
aar_f2017:fnr06     60.036   1089.704   0.055 0.956069    
aar_f2009:fnr07    134.353   1525.051   0.088 0.929808    
aar_f2010:fnr07    728.914   1525.112   0.478 0.632745    
aar_f2011:fnr07    275.017   1525.266   0.180 0.856930    
aar_f2012:fnr07   1047.940   1525.235   0.687 0.492122    
aar_f2013:fnr07    890.998   1525.236   0.584 0.559173    
aar_f2014:fnr07    582.123   1525.332   0.382 0.702772    
aar_f2015:fnr07    990.944   1525.354   0.650 0.515996    
aar_f2016:fnr07    447.813   1525.278   0.294 0.769099    
aar_f2017:fnr07    960.018   1525.236   0.629 0.529146    
aar_f2009:fnr08    329.317   1240.237   0.266 0.790631    
aar_f2010:fnr08   1281.636   1240.345   1.033 0.301597    
aar_f2011:fnr08    646.495   1240.336   0.521 0.602269    
aar_f2012:fnr08   1090.416   1240.413   0.879 0.379470    
aar_f2013:fnr08    575.599   1240.249   0.464 0.642628    
aar_f2014:fnr08    689.084   1240.251   0.556 0.578548    
aar_f2015:fnr08   -776.910   1240.290  -0.626 0.531130    
aar_f2016:fnr08  -1716.491   1240.468  -1.384 0.166595    
aar_f2017:fnr08  -2045.538   1240.415  -1.649 0.099294 .  
aar_f2009:fnr09    686.715   1288.922   0.533 0.594245    
aar_f2010:fnr09    986.486   1288.914   0.765 0.444149    
aar_f2011:fnr09    599.582   1288.944   0.465 0.641860    
aar_f2012:fnr09   1071.846   1289.011   0.832 0.405779    
aar_f2013:fnr09     64.585   1289.204   0.050 0.960050    
aar_f2014:fnr09   -186.541   1289.179  -0.145 0.884965    
aar_f2015:fnr09  -1242.730   1289.232  -0.964 0.335201    
aar_f2016:fnr09  -1987.219   1289.181  -1.541 0.123368    
aar_f2017:fnr09  -3223.036   1289.344  -2.500 0.012510 *  
aar_f2009:fnr10    231.288   1199.909   0.193 0.847172    
aar_f2010:fnr10    924.121   1199.916   0.770 0.441302    
aar_f2011:fnr10    168.648   1199.944   0.141 0.888243    
aar_f2012:fnr10    321.458   1200.216   0.268 0.788856    
aar_f2013:fnr10   -515.180   1200.200  -0.429 0.667793    
aar_f2014:fnr10   -674.319   1200.339  -0.562 0.574335    
aar_f2015:fnr10  -1492.749   1200.502  -1.243 0.213856    
aar_f2016:fnr10  -3090.918   1200.777  -2.574 0.010124 *  
aar_f2017:fnr10  -3807.142   1200.767  -3.171 0.001545 ** 
aar_f2009:fnr11   -414.412   1069.772  -0.387 0.698515    
aar_f2010:fnr11    642.468   1069.866   0.601 0.548235    
aar_f2011:fnr11   1243.418   1070.024   1.162 0.245359    
aar_f2012:fnr11   1467.212   1070.665   1.370 0.170728    
aar_f2013:fnr11   1179.371   1071.062   1.101 0.270979    
aar_f2014:fnr11   -183.391   1071.523  -0.171 0.864124    
aar_f2015:fnr11  -1489.385   1072.451  -1.389 0.165063    
aar_f2016:fnr11  -3274.743   1072.946  -3.052 0.002303 ** 
aar_f2017:fnr11  -3863.610   1073.185  -3.600 0.000326 ***
aar_f2009:fnr12     21.853   1036.805   0.021 0.983186    
aar_f2010:fnr12    381.898   1036.801   0.368 0.712658    
aar_f2011:fnr12    165.379   1036.901   0.159 0.873297    
aar_f2012:fnr12    669.171   1037.128   0.645 0.518864    
aar_f2013:fnr12    -69.430   1037.183  -0.067 0.946636    
aar_f2014:fnr12   -147.825   1037.277  -0.143 0.886690    
aar_f2015:fnr12   -711.755   1037.476  -0.686 0.492767    
aar_f2016:fnr12   -901.775   1037.688  -0.869 0.384941    
aar_f2017:fnr12  -2046.447   1038.104  -1.971 0.048828 *  
aar_f2009:fnr14   -220.698   1663.985  -0.133 0.894498    
aar_f2010:fnr14    536.844   1663.957   0.323 0.747009    
aar_f2011:fnr14   1984.847   1664.012   1.193 0.233090    
aar_f2012:fnr14   1739.551   1664.177   1.045 0.296018    
aar_f2013:fnr14    208.353   1664.208   0.125 0.900381    
aar_f2014:fnr14    253.302   1664.812   0.152 0.879084    
aar_f2015:fnr14  -1695.187   1665.139  -1.018 0.308783    
aar_f2016:fnr14  -1552.417   1665.259  -0.932 0.351330    
aar_f2017:fnr14  -2074.192   1665.271  -1.246 0.213077    
aar_f2009:fnr15    205.720    998.429   0.206 0.836779    
aar_f2010:fnr15    548.008    998.671   0.549 0.583249    
aar_f2011:fnr15    463.880    998.884   0.464 0.642414    
aar_f2012:fnr15    463.860    999.265   0.464 0.642556    
aar_f2013:fnr15      7.994    999.213   0.008 0.993617    
aar_f2014:fnr15   -481.056    999.093  -0.481 0.630220    
aar_f2015:fnr15   -587.449    999.385  -0.588 0.556727    
aar_f2016:fnr15  -1872.887    999.582  -1.874 0.061126 .  
aar_f2017:fnr15  -2799.827    999.681  -2.801 0.005149 ** 
aar_f2009:fnr16   -346.631   1069.772  -0.324 0.745955    
aar_f2010:fnr16   -237.962   1069.934  -0.222 0.824020    
aar_f2011:fnr16   -497.945   1069.952  -0.465 0.641705    
aar_f2012:fnr16    380.682   1070.437   0.356 0.722154    
aar_f2013:fnr16   -347.235   1070.757  -0.324 0.745754    
aar_f2014:fnr16   -229.362   1070.812  -0.214 0.830418    
aar_f2015:fnr16   -139.973   1070.880  -0.131 0.896019    
aar_f2016:fnr16  -1074.143   1070.970  -1.003 0.316004    
aar_f2017:fnr16  -2278.453   1070.923  -2.128 0.033499 *  
aar_f2009:fnr17   -288.412   1288.940  -0.224 0.822969    
aar_f2010:fnr17   -422.338   1289.001  -0.328 0.743214    
aar_f2011:fnr17    257.671   1289.086   0.200 0.841590    
aar_f2012:fnr17    637.493   1289.624   0.494 0.621133    
aar_f2013:fnr17    203.405   1289.762   0.158 0.874704    
aar_f2014:fnr17    -61.073   1289.824  -0.047 0.962239    
aar_f2015:fnr17   -867.834   1289.740  -0.673 0.501107    
aar_f2016:fnr17  -1612.215   1290.487  -1.249 0.211703    
aar_f2017:fnr17  -2761.733   1290.527  -2.140 0.032479 *  
aar_f2009:fnr18   -148.285   1089.412  -0.136 0.891744    
aar_f2010:fnr18    402.939   1089.510   0.370 0.711545    
aar_f2011:fnr18    252.454   1089.674   0.232 0.816812    
aar_f2012:fnr18    482.679   1089.761   0.443 0.657871    
aar_f2013:fnr18    201.272   1090.026   0.185 0.853524    
aar_f2014:fnr18   -393.115   1090.258  -0.361 0.718459    
aar_f2015:fnr18   -439.127   1090.372  -0.403 0.687190    
aar_f2016:fnr18  -1361.291   1090.771  -1.248 0.212178    
aar_f2017:fnr18  -2661.041   1090.689  -2.440 0.014785 *  
aar_f2009:fnr19    453.061   1872.733   0.242 0.808864    
aar_f2010:fnr19    982.125   1872.779   0.524 0.600045    
aar_f2011:fnr19   -669.729   1872.850  -0.358 0.720682    
aar_f2012:fnr19    727.671   1872.902   0.389 0.697670    
aar_f2013:fnr19    278.261   1873.128   0.149 0.881921    
aar_f2014:fnr19   1688.165   1873.121   0.901 0.367563    
aar_f2015:fnr19    369.085   1873.412   0.197 0.843839    
aar_f2016:fnr19    906.286   1873.612   0.484 0.628646    
aar_f2017:fnr19   -716.410   1873.886  -0.382 0.702272    
aar_f2009:fnr20   -927.061   1664.164  -0.557 0.577542    
aar_f2010:fnr20   -547.207   1664.063  -0.329 0.742313    
aar_f2011:fnr20   -542.321   1664.293  -0.326 0.744568    
aar_f2012:fnr20   -378.342   1664.741  -0.227 0.820240    
aar_f2013:fnr20  -1110.163   1664.836  -0.667 0.504960    
aar_f2014:fnr20  -1563.827   1665.176  -0.939 0.347778    
aar_f2015:fnr20  -3266.760   1665.444  -1.961 0.049964 *  
aar_f2016:fnr20  -3169.910   1665.821  -1.903 0.057200 .  
aar_f2017:fnr20  -3922.387   1665.464  -2.355 0.018615 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2105 on 1944 degrees of freedom
Multiple R-squared:  0.8953,    Adjusted R-squared:  0.8848 
F-statistic: 85.21 on 195 and 1944 DF,  p-value: < 2.2e-16

iii.

pm2 <- pm2 %>%
  mutate(res_m2 = resid(lm2))

iv.

Delplott:

pm2 %>% filter(fnr %in% c("01", "02", "04", "11", "12")) %>%
ggplot(mapping = aes(x = aar_d, y = res_m2)) +
geom_line(aes(group = knavn)) +
scale_size_manual(values = c(seq(2.0, 0.5, by = -0.1))) +
geom_hline(yintercept = 0) +
theme(legend.position = 'bottom') +
  facet_wrap(~fylke)

i & ii.

Kvaliteten på modellen er ikke helt optimal da den mangler noen variabler. Dette kan ha noe med heteroskedatisitet i modell at det er stor variasjon. Det er store residualer, spesielt i Rogaland.

Ut i fra grafene så ser man at variasjonen er stor. Dette indikerer et heteroskedastisitetsproblem, og dermed er det grunn til at det er utelatte viktige variabler (brudd på TS.3/TS’.3)

iii.

pm2 %>% filter(fnr %in% c("11")) %>%
ggplot(mapping = aes(x = aar_d, y = res_m2)) +
scale_color_viridis(discrete = TRUE, option = "D") +
geom_line(aes(group = knavn, colour = knavn, size =knavn)) +
scale_size_manual(values = c(seq(2.0, 0.5, by = -0.1))) +
geom_hline(yintercept = 0) +
theme(legend.position = 'bottom')

i.

pm2 %>% filter(knr %in% c("1119", "1120", "1127", "1121", "1130", "1135", "1106", "1149")) %>%
ggplot(mapping = aes(x = aar_d, y = res_m2)) +
scale_color_viridis(discrete = TRUE, option = "H") +
geom_line(aes(group = knavn, colour = knavn, size =knavn)) +
scale_size_manual(values = c(seq(2.0, 0.5, by = -0.1))) +
geom_hline(yintercept = 0) +
theme(legend.position = 'bottom')

ii.

Stavanger-kommunene overvurderes (Hå, Klepp og Randaberg).

Modell for hvert år

i.

pm2_n <- pm2 %>% 
  group_by(aar) %>%
  select(pm2, fnr, knr, aar, aar_f, Menn_ya_p, Kvinner_ya_p, Total_ya_p, inc_k1, inc_k5, uni_k_mf, uni_l_mf, Trade_pc_100K) %>% 
  nest()

pm2_n

pm2_n$data[[1]] %>%
head(n = 5)

dim(pm2_n)

[1] 10  2

1.

kom_model <- function(a_df) {
  lm(pm2 ~ fnr + Total_ya_p + inc_k1 + inc_k5 + uni_k_mf + uni_l_mf + Trade_pc_100K, data = pm2)
}

pm2_n <- pm2_n %>% 
  mutate(model = map(data, .f = kom_model)) 

kom_model(pm2_n$aar) %>% 
  summary()

Call:
lm(formula = pm2 ~ fnr + Total_ya_p + inc_k1 + inc_k5 + uni_k_mf + 
    uni_l_mf + Trade_pc_100K, data = pm2)

Residuals:
     Min       1Q   Median       3Q      Max 
-10648.8  -1602.8   -168.1   1474.5  14320.1 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)    6480.17    2872.86   2.256 0.024194 *  
fnr02           151.87     314.23   0.483 0.628913    
fnr03          7275.88     959.78   7.581 5.11e-14 ***
fnr04         -2866.03     317.21  -9.035  < 2e-16 ***
fnr05         -2728.80     305.31  -8.938  < 2e-16 ***
fnr06         -2048.90     312.29  -6.561 6.70e-11 ***
fnr07          -198.84     434.89  -0.457 0.647557    
fnr08         -3439.76     356.42  -9.651  < 2e-16 ***
fnr09         -2211.31     367.84  -6.012 2.16e-09 ***
fnr10         -1357.67     346.79  -3.915 9.33e-05 ***
fnr11          -354.75     345.19  -1.028 0.304213    
fnr12         -1067.22     318.04  -3.356 0.000806 ***
fnr14         -3685.59     483.41  -7.624 3.68e-14 ***
fnr15         -3897.81     307.47 -12.677  < 2e-16 ***
fnr16         -2039.39     304.44  -6.699 2.69e-11 ***
fnr17         -3222.93     376.12  -8.569  < 2e-16 ***
fnr18         -2229.33     316.67  -7.040 2.59e-12 ***
fnr19         -2938.14     530.36  -5.540 3.40e-08 ***
fnr20         -4283.12     477.15  -8.976  < 2e-16 ***
Total_ya_p      136.67      42.46   3.219 0.001306 ** 
inc_k1         -387.33      33.05 -11.720  < 2e-16 ***
inc_k5           42.66      26.93   1.584 0.113318    
uni_k_mf        278.27      34.36   8.099 9.28e-16 ***
uni_l_mf       1030.52      50.75  20.305  < 2e-16 ***
Trade_pc_100K  1075.31     238.65   4.506 6.97e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2639 on 2115 degrees of freedom
Multiple R-squared:  0.8209,    Adjusted R-squared:  0.8189 
F-statistic: 403.9 on 24 and 2115 DF,  p-value: < 2.2e-16

i.

pm2_n %>% 
  filter(aar%in% c("2008")) %>% 
  .$model %>% 
  map_df(glance) %>% 
  print()

mod_sum <- pm2_n %>% 
  filter(aar %in% c("2008", "2009", "2010", "2011", "2012", "2013", "2014", "2015", "2016", "2017")) %>% 
  mutate(mod_summary = map(.x = model, .f = glance)) %>% 
  unnest(mod_summary) %>% 
  print()

coef_df <- mod_sum$model %>% 
  map_df(1) %>% 
  as.tibble()